Multiply the following complex numbers: $({-3+i}) \cdot ({-1-4i})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-3+i}) \cdot ({-1-4i}) = $ $ ({-3} \cdot {-1}) + ({-3} \cdot {-4}i) + ({1}i \cdot {-1}) + ({1}i \cdot {-4}i) $ Then simplify the terms: $ (3) + (12i) + (-1i) + (-4 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 3 + (12 - 1)i - 4i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 3 + (12 - 1)i - (-4) $ The result is simplified: $ (3 + 4) + (11i) = 7+11i $